Refined multilayered beam, plate and shell elements based on Jacobi polynomials

Carrera, Erasmo; Augello, R.; Pagani, Alfonso; Scano, D.

doi:10.1016/j.compstruct.2022.116275

Cited by 23 publications

(6 citation statements)

References 42 publications

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“…For the transverse displacements, the proposed FEs are demonstrated to be reliable with respect to the reference solutions. In particular, the properties of the Lagrange and Jacobi polynomials to build higher order structural theories have been detailed in Carrera et al 43 Some of the remarks arising from that paper apply to the problem considered in this work, where the same polynomials are used to build several FEs. In fact, given a polynomial order, the results do not depend on the type of the employed polynomial.…”

Section: Discussionmentioning

confidence: 99%

“…In this method, it is possible to increase both the number of elements, see Zhu and Zienkiewicz, 41 and the polynomial order of the shape function, see Babuška et al 42 Based on CUF, the present research introduces a new class of unified beam, plate and shell FEs based on Jacobi shape functions, with particular emphasis on the attenuation of numerical locking issues. Jacobi polynomials were used to generate high order theories of structures in the framework of CUF in an axiomatic/asymptotic manner, see Carrera et al 43 Low-order to very refined models were implemented. The latter were demonstrated to approximate the numerical and exact solutions in a very precise manner, eventually showing some interesting properties if compared to CUF-based Higher-Order Theories (HOT) employing Lagrange and Maclaurin thickness functions; see References 44-47.…”

Section: Introductionmentioning

confidence: 99%

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Finite elements based on Jacobi shape functions for the analysis of beams, plates and shells

Pagani

Carrera

Scano

et al. 2023

Numerical Meth Engineering

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This paper proposes the use of Jacobi polynomials to approximate higher‐order theories of beam, plate, and shell structures. The Carrera unified formulation is used in this context to express displacement kinematics in a hierarchical form. In this manner, classical to complex higher‐order theories can be implemented with ease. Particular attention is focused on the attenuation and the correction of the shear locking. Therefore, reduced integration as well as mixed interpolation of tensorial components methods are investigated against the new finite elements. Several case studies are taken into account to highlight the effectiveness and robustness of the proposed approach. Also, several benchmarks are provided for future assessments.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finite elements based on Jacobi shape functions for the analysis of beams, plates and shells

Pagani

Carrera

Scano

et al. 2023

Numerical Meth Engineering

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“…Beam-forming algorithms adjust beam direction based on user device feedback, enhancing adaptation to changing conditions, user movements, and interference levels. [133] Interference Mitigation…”

Section: Narrow-band and Wide-band Beam-formingmentioning

confidence: 99%

Review of Joint Radar, Communication, and Integration of Beam-forming Technology

HUSSAIN,

2024

Preprint

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In this paper, we dive into the exciting world of wireless communication, focusing on how millimeter-wave technology and Multiple-Input Multiple-Output phased array antennas are shaping the future of 5G and the upcoming 6G technologies. We cover the latest advancements in millimeter-wave and beam-forming technologies, emphasizing their role in enhancing network security and efficiency in automotive vehicles through dual radar communication. Our discussion spans the benefits, applications, challenges, and solutions of these technologies individually from millimeter-wave to beam-forming technology and joint radar communications, alongside a look at their theoretical and practical implementations. We emphasize the integration of beam-forming technology in joint radar communications for future automotive vehicles and its impact on automotive systems, smart cities, and the Internet of Things (IoT). Looking ahead, we discuss the potential of these technologies to transform future tech landscapes, while also addressing the security implications of merging communication and radar capabilities. This paper aims to provide a clear view of the advancements and prospects of millimeter-wave, beam-forming, and dual radar communication technologies.

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“…To address those limitations, many advanced beam theories (Berdichevsky et al., 1992; El Fatmi and Zenzri, 2002; Silvestre and Camotim, 2002) have been put forward in the past years, including Carrera Unified Formulation (CUF) proposed by Carrera and Giunta (2010). This higher-order 1D model allows for the use of different cross-sectional expansion polynomials, such as Taylor polynomials (Carrera et al., 2013), Lagrange expansion (Pagani et al., 2021), and Jacobi polynomials (Carrera et al., 2023), to evaluate 3D displacement field. The CUF beam theory allows for the selection of the desired beam and expansion order, providing higher efficiency and lower computational costs.…”

Section: Introductionmentioning

confidence: 99%

A consistent crack bandwidth for higher-order beam theories: Application to concrete

Shen,

Tiago Arruda,

Pagani

2023

International Journal of Damage Mechanics

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Higher-order theories have a broad range of successful applications but also suffer from localization instability and mesh-size dependency when modeling quasi-brittle materials such as concrete with strain-softening behavior. To overcome the above difficulties, this paper proposes a fracture energy regularization method with a unified, consistent crack bandwidth specifically tailored for higher-order beam theories. The Carrera unified formulation (CUF) is applied to develop scalable structural theories and related finite elements. To evaluate the accuracy of the new crack bandwidth, three typical experimental quasi-static benchmarks of pure concrete structures are utilized. A modified Mazars damage model with tensile and compressive softening laws is implemented in these benchmarks. The comparison between numerical and experimental results demonstrates that the proposed method can accurately determine the correct crack bandwidth and preserve the dissipated energy per unit area of a fracture surface. Moreover, this robust estimation of crack bandwidth reduces the mesh dependency in general, ensuring the high efficiency of the CUF model.

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Refined multilayered beam, plate and shell elements based on Jacobi polynomials

Cited by 23 publications

References 42 publications

Finite elements based on Jacobi shape functions for the analysis of beams, plates and shells

Finite elements based on Jacobi shape functions for the analysis of beams, plates and shells

Review of Joint Radar, Communication, and Integration of Beam-forming Technology

A consistent crack bandwidth for higher-order beam theories: Application to concrete

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